We study the effects of stochastic birth and death processes on the structural phases of systems of active and passive Brownian particles subject to volume exclusion. The total number of particles in the system is a fluctuating quantity, determined by the birth and death parameters and on the activity of the particles. As the birth and death parameters are varied, we find liquid, hexatic, and solid phases. For passive particles, these phases are found to be spatially homogeneous. For active particles, motility-induced phase separation (coexisting hexatic and liquid phases) occurs for large activity and sufficiently small birth rates. We also observe a reentrant transition to the hexatic phase when the birth rate is increased. This results from a balance of an increasing number of particles filling the system, and a larger number of defects resulting from the birth and death dynamics.